Potential Difference (V)

• Charge flows from higher potential to lower potential until electric potential equilibrium is reached.

• When electric potential is zero (equilibrium), current flow stops.

Electric Current• Electrical charge in motion is electric current.• Current is measured by counting the amount of

charges that pass a given point per second

Symbol variable Unit

I current A (amp)

1 1Cs A

Comparing a DC circuit to Flow of Water

http://faraday.physics.utoronto.ca/IYearLab/Intros/DCI/Flash/WaterAnalogy.html

•What component in the electrical circuit is equivalent to the pump in the animation?

Direct Current (DC)• DC stands for direct current. Here current only travels in

one direction.

Current vs. Time (DC)

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

Time (s)

Cu

rren

t (A

)

Alternating Current (AC)• AC stands for alternating current. Here current switches

directions at a set frequency.

Current vs. Time (AC)

-1.5

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4

Time (s)

Cu

rren

t (A

)

• AC stands for alternating current. Here current switches directions at a set frequency.

Alternating Current (AC)

Voltage• Current flows only when there is a potential

difference (V)• Voltage sources can sustain a potential difference• Voltage in a circuit is analogous to pressure in a

water hose.

Voltage Source

OFF ON

1 1 JCV

Voltage Sources• There are different types of devices that can provide a

source of voltage.• Sources that provide DC include:

– Batteries– DC Power Supplies– DC Generators

• Sources that provide AC include:– Electrical Outlets– Alternators– Power Inverters

Electric Circuits• Electric current flows very well if there is a complete loop for

charge to flow. This is called an electrical circuit.• Circuits often contain various elements, giving it practical use.

Examples of circuit elements include:– Switches– Sources of Resistance (Such as a Light)– Meters

Circuit Symbols• Each circuit element has its own symbol. • Common circuit symbols are shown below.

Resistor

Switch

Wire Battery

Voltmeter

Ammeter

A Conductor of Current

Opens and Closes Circuits

Provides Resistance to Current Flow

Source of DC Charge Flow

Measures Current

Measures Voltage

More Circuit Symbols• Here are some additional circuit symbols that you may see.

Potentiometer

AC Source

Ground

Crossing

Junction

Capacitor DiodeStores Charge on Plates

Variable Resistor

Provides AC Current

Drains Excess Charge Buildup

Only Allows Current to Flow One Way

All Four Wires Connect

Wires Only Cross and do not Connect.

Electrical Resistance• Every circuit contains some resistance to current flow.• This is due to imperfections in the crystalline lattice

structure of the conductor.• Imagine the lattice structure below is the atoms in a wire.• Notice how the moving electrons experience resistance.• The variable for resistance is R.• The unit for resistance is the Ohm (symbol ).

Electrical ResistanceL

RA

(1 )oR R T

R resistance (Ohm) W

resistively (m)

L Length (m)

A area m2

(1 )o T

Ohm’s Law• The current in a circuit is directly proportional to voltage

and inversely proportional to resistance.

• This relationship is known as Ohm’s Law.

VR

I

Resistance ()

Voltage (V)

Current (A)

I V 1 I

R

Sample Problem (Ohm’s Law)• A toaster is connected to a 120V outlet and draws 3A of

electrical current.• What is the resistance of the toaster? V

RI

120

3.0

VR

A

40R

Power and Electricity• There are also two useful equations that relate power to

electrical quantities.

• Notice how current is squared in the second equation. Increasing current in a circuit drastically increases the power consumed.

• High current wires generate heat.• This is why electricity transferred over large distances is

at high voltage and not high current. Otherwise, the power losses would be very wasteful.

P VI 2P I R

Sample Problem (Electrical Power)• Remember the toaster from a previous problem?• What is the power consumed by the toaster?• If it takes 45s for the toast to be made, how much energy

was consumed?P VI

120 3.0P V A360P W

EP E Pt

t

360 45E W s

16,200E J

120V V3.0I A

Given

Resistance of power lines is .2 ohms per Km

How much power is lost during transmission if a home 3.5Km from the power plant cooks on a stove that draws 41A?

How can energy loss be reduced?

Either reduce I or R

R is a fix physical property

2

2

2( )*.2 / (3.5 )

1.4

41 (1.4 )

R wires km km

R

P I R

P A

2350p W

P VI

High voltage lines transmit power between 500,000V-750,000V to reduce energy loss. 2350

750,000

WI

V

.0031I A

2(.0031 ) (1.4 )lossP A

51.34 10lossP x W

2350

Original loss

P W

The Kilowatt Hour• Did you ever read an electric bill?• You are charged for the number of kilowatt

hours used during the month.• This is energy, not power, because:

• The amount of kilowatt-hours gets multiplied times a rate to find the overall energy cost.

E Pt kWh

Power (kW) Time (h)

C RECost ($)

Rate $kWh

Energy (kWh)

1kW =1000W

How Much Energy is a kWh?• We all know that the SI unit for energy is the Joule (J). • How many Joules are there in one kilowatt hour?

1 1000 1000 JskW W

1 3600h sE Pt

1000 3600JsE s

3,600,000E J 63.6 10E J or

Sample Problem (KWh)• During the winter, an electric heater runs 8 hours every

day over the course of a month (30 days). • The power consumed by the heater is 1200W.• How many kWh of energy are consumed?• If the rate is $0.11 per kWh, then what is the cost to

operate the heater?

C RE

1.2 240E kW h288E kWh

8 30 240t h h

$0.11 288kWhC kWh$31.68C

1200 1.2W kW